Question

You have 10 shirts, 9 pants, and 4 belts. How many outfits can you make out of these? (Assume all colors are perfectly coordinated.)

Answer 1

You Haven't mentioned which method should i solve hence i solved in Both method use only one which you are required

1) Answer Using Combination,
Total number of shirts=10

Total number of Pants = 9

Total number of Belts =b

Ways of selecting one Shirt= 10C1​=10

Ways of selecting one Pant= 9C1​=9

Ways of selecting one Belt= 4C1​=4

Number of different outfits that can be made=10×9×4=360

Number of different outfits that can be made=360 Outfits

2) Answer Using Counting Principle:

For every one of 10 shirts, I can wear one of 4 belts...so that is 40 different combinations.
For every pair of pants, he can wear any of the 40 combos of shirt and belt. Since he has 9 pair of pants, 9 times 40 gives the same 360 combinations.

Principle:
If first thing can be done in m1 ways and second thing can be done in m2 ways then both things together can be done together in m1*m2 ways.

hence,
the process can be done in m1*m2*m3*...*mk ways

Assuming m1= 10 shirts

m2= 9 pants

m3 = 4 belts

-------------------------------------
therefore,
no. of combinations (or Outfits ) is 10*9*4 = 360 ways

If any Doubt or Question then put in comment.